An analysis of the SDO AIA observations of oscillations in a sunspot with a duration of 6 h has shown that powerful umbral flashes occur in local oscillation cells. The local oscillation spectrum has been found to be distorted by the short pulses produced by powerful flashes. For one of the single flashes we have managed to extract the undistorted local oscillation spectrum for this cell. The flash has turned out to occur against the background of local 3-min oscillations. A comparison of the observations in the 1600 and 1700 Å channels has shown that the most powerful flashes occur at the level of the upper photosphere below the temperature minimum. Powerful umbral flashes are observed in the form of single or recurrent short pulses with an interval of ̃20 min. This distinguishes them from the long-known less powerful flashes that are trains of pulses with intervals of ̃3 min. Both types of flashes find their explanation in terms of the hypothesis about the existence of a slow-wave subphotospheric resonator and various modes of its operation.